Two U.S. officials briefed on this latest intelligence from the region, Censor.NET reports citing Fox News.
Meanwhile, U.S. Navy Captain Jeff Davis told reporters a U.S. aircraft flying over Syria had to be rerouted to avoid a Russian fighter jet at least once.
"We have taken action to maintain safe separation," Davis said, adding that the U.S. aircraft "changed path a little bit." He did not disclose which type of U.S. aircraft was involved.
U.S. officials tell Fox News the drone encounters took place over ISIS-controlled Syria, including its de facto headquarters in Raqqa, as well as along the Turkish-Syrian border near Korbani. Another occurred in the northwest, near the highly contested city of Aleppo.
"The first time it happened, we thought the Russians got lucky. Then it happened two more times," said one official.
The U.S. military's MQ-1 Predator drone is not a stealth aircraft.
This development comes as Russia has moved some of its Mi-24 gunships and transport helicopters from an air base along the Mediterranean to another air base outside Homs, roughly 100 miles away. Russian ground forces, hundreds of Russian marines -- as well as four BM-30 Smerch rocket launchers capable of firing cluster munitions, mines as well as high explosive warheads -- are now in position to strike, but there is no evidence they have done so according to multiple defense officials. Infantry fighting vehicles and more a conventional artillery battery has also been seen by the intelligence community.
All these movements demonstrate the Russians are forming a "protective belt" around Latakia, the stronghold of Syrian President Bashar Assad, and are carrying out airstrikes against anti-Assad rebel forces, some backed by the CIA, to protect both regime and Russian interests, including a Russian naval base in Tartus established in the 70s.
Read more: Only two out of 57 Russian bombardments targeted ISIL, Turkish Prime Minister says
The Pentagon maintains the vast majority of strikes from its forward operating base at Bassel al-Assad airport in Latakia including some 30 fighter/bomber jets have been against Syrian opposition forces and not ISIS, and one official pushed back on Russian defense ministry claims on the number of strikes the Russians have launched.
"The Russians carried out only one half or at best a quarter of the strikes they claim to have conducted," said a senior military official.
"It is easy to see a predator on radar," said one official.
The Russians have not attempted to shoot down any of the U.S. drones, but instead have flown "intercept tracks," a doctrinal term meaning the Russians flew close enough to make their presence felt, according to one official.
One other official said, "the Russians flew very close, but did not impede the drone flight."
Related materials: War in Syria